Study of a quantum fermi-acceleration model

We consider the problem of a free particle in a rigid box with one wall fixed and the other oscillating periodically in time. The spectral properties of the evolution operator are calculated. We find that by a tuning of Planck's constant, the statistics of the quasienergy spectrum go continuously from showing Poisson to Gaussian-orthogonal-ensemble-like properties. This change is related to a transition from localized to extended states in energy space. We make the conjecture that recent results of microwave excitations on quasi one-dimensional highly excited hydrogen atoms may be related to this work.

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